本书是一本英文原版影印版专著，二次剩余的概念最早出现于欧拉1754年发表的论文中，1783年欧拉明确地叙述了二次互反律，二次互反律的各种角度的推广是构成近代数论的一项重要内容。本书主要包括二次互反律的赫克证明、高斯和、相对二次互反律、诺依曼定理、局部紧致阿贝尔情形、海森堡群、酉算子群、π的核心、局部域的矢量空间、局部域的四元法、久保田和上同调、辛群的双面、希尔伯特互反律等内容。本书适合二次互反律专业的大学生或研究生参考阅读。

PREFACE
ACKNOWLEDGMENTS
INTRODUCTION
1. Hecke's Proof of Quadratic Reciprocity
1.1 Hecke 9-functions and Their Functional Equation
1.2 Gauss(-Hecke) Sums
1.3 Relative Quadratic Reciprocity
1.4 Endnotes to Chapter 1
2.Two Equivalent Forms of Quadratic Reciprocity
3.The Stone-Von Neumann Theorem
3.1 The Finite Case:A Paradigm
3.2 The Locally Compact Abelian Case: Some Remarks
3.3 The Form of the Stone-Von Neumann Theorem Used
in 8 4
4.Weil's"Acta"Paper
4.1 Heisenberg Groups
4.2 A Heisenberg Group and A Group of Unitary
Operators
4.3 The Kernel of T
4.4 Second-Degree Characters
4.5 The Splitting of T on a Distinguished Subgroup of
B(G)
4.6 Vector Spaces Over Local Fields
4.7 Quaternions Over a Local Field
4.8 Hilbert Reciprocity
4.9 The Stone-Von Neumann Theorem Revisited
4.10 The Double Cover of the Symplectic Group
4.11 Endnotes to Chapter 4
5.Kubota and Cohomology
5.1 Weil Revisited
5.2 Kubota's Cocycle
5.3 The Splitting of a Over SL(2,k)
5.4 2-Hilbert Reciprocity Once Again
6.The Algebraic Agreement Between the Formalisms of Weil
and Kubota
6.1 The Gruesome Diagram
6.2 The Even More Gruesome Diagram
7.Hecke's Challenge: General Reciprocity and Fourier
Analysis on the March
BIBLIOGRAPHY
INDEX
编辑手记